Let f : C → C be an entire map of the form f(z) = P (z) exp(Q(z)), where P and Q are polynomials of arbitrary degrees (we allow the case Q = 0). Building upon a method pioneered by M. Shishikura, we show that if f has a Siegel disk of bounded type rotation number centered at the origin, then the boundary of this Siegel disk is a quasicircle containing at least one critical point of f . This uni...

Kerr parametric oscillators (KPOs), which can be implemented with superconducting parametrons possessing large nonlinearity, have been attracting much attention in terms of their applications to quantum annealing, universal computation, and studies many-body systems. It is practical importance for these realize fast accurate tunable coupling between KPOs a simple manner. We develop scheme high ...

Quantum-dot cellular automata (QCA) technology is believed to be a good alternative CMOS technology. This nanoscale can provide platform for design and implementation of high performance power efficient logic circuits. However, the fabrication QCA circuits susceptible faults appearing in this form missing cells, additional rotated cells displaced cells. Over years, several solutions have been p...

If the rotation angle α is irrational, then ζ is generating for T (see [4]) and the partition ζn = ζ ∨Tζ ∨···∨Tn−1ζ is made out of 2n arcs. This can be easily realized by induction: when passing from ζn−1 to ζn one has to add to the endpoints of the arcs belonging to ζn−1 the two new points Tn(0) and Tn(1/2) (for rational α, say α = p/q, the partition ζn has precisely 2q arcs for all n≥ q). Thu...

Notation We denote the Riemann sphere C U {00} by § 2 and for a e U, we denote by R a :z >e 2nia z the rotation of § 2 of rotation number a with fixed points 0 and 00. On S 2 c W we put the standard induced metric d; and for / > 0 the /-ball with centre x is {ye § 2 :d(x, y) < /}. On subsets of § 2 we put the induced topology. Given A c= § 2 we denote the e-neighbourhood of A by = {ye §*:d(y,A)...

The main objective of this paper is to implement all digital modulation techniques into a single module and implement in a Field Programmable Gate Array (FPGA). The proposed system allows the user to select any one of four modulations without reconfiguring the FPGA. Carrier waveform for the modulator is generated using coordinate rotation digital computer CORDIC algorithm which uses shift, addi...

Neutral atoms are promising for large-scale quantum computing, but accurate neutral-atom entanglement depends on large Rydberg interactions which strongly limit the interatomic distances. Via a phase accumulation in detuned Rabi cycles enabled by interaction of similar magnitude to frequency, we study controlled-phase gate with an arbitrary and extend it controlled-not gate. The gates need only...

We consider brightness/contrast-invariant and rotation-discriminating template matching that searches an image to analyze A for a query image Q. We propose to use the complex coefficients of the discrete Fourier transform of the radial projections to compute new rotation-invariant local features. These coefficients can be efficiently obtained via FFT. We classify templates in “stable” and “unst...

In the title compound, C21H22N2O, the planes of the two six-membered rings make a dihedral angle of 89.51 (7)°. The pyrrolidine ring has a puckering amplitude q 2 = 0.418 (3) and a pseudo-rotation phase angle ϕ2 = -166.8 (5), adopting a twist conformation (T). The other five-membered ring has a puckering amplitude q 2 = 0.247 (2) and a pseudo-rotation phase angle ϕ2 = -173.7 (5), adopting an en...